We demonstrate unambiguously that the field enhancement near the apex of a laser-illuminated silicon tip decays according to a power law that is moderated by a single parameter characterizing the tip sharpness. Oscillating the probe in intermittent contact with a semiconductor nanocrystal strongly modulates the fluorescence excitation rate, providing robust optical contrast and enabling excellent background rejection. Laterally encoded demodulation yields images with <10 nm spatial resolution, consistent with independent measurements of tip sharpness. DOI: 10.1103/PhysRevLett.93.180801 PACS numbers: 07.79.Fc, 42.50.Hz, 61.46.+w, 78.67.Bf The potential of near-field microscopy to optically resolve structure well below the diffraction limit has excited physicists, chemists, and biologists for almost 20 years. Conventional near-field scanning optical microscopy (NSOM) uses the light forced through a small metal aperture to locally excite or detect an optical response. The spatial resolution in NSOM is limited to 30 -50 nm by the penetration depth of light into the metal aperture. More recently, apertureless-NSOM (ANSOM) techniques were developed which leverage the strong enhancement of an externally applied optical field at the apex of a sharp tip for local excitation of the sample [1][2][3][4][5][6][7][8][9][10][11]. The promised advantage of ANSOM is that spatial resolution should be limited only by tip sharpness (typically 10 nm). The resolution in most previous ANSOM experiments, however, was at best marginally better than NSOM and was inferior to expectations based on tip sharpness alone. Further, the external field used to induce enhancement led to a substantial background signal and to assertions that one-photon fluorescence is not appropriate for ANSOM [12,13]. These experiments fell short of their potential because they maintained a tip-sample gap of several nanometers, and thus did not thoroughly exploit the tightly confined enhancement.Here, we demonstrate an ANSOM technique that fully exploits the available contrast and leads to spatial resolution that is limited only by tip sharpness. The problems associated with a tip-sample gap are overcome by oscillating the probe in intermittent contact with the sample. The detected signal is then composed of a modulated near-field portion that is superimposed on the far-field background. Subsequent demodulation decouples the two components and thus strongly elevates the near-field signal relative to the background. With this technique, we measured <10 nm lateral resolution via one-photon fluorescence imaging of isolated quantum dots, consistent with independent measurements of tip sharpness. The measured resolution is >3 times better than previous reports for quantum dots using one-photon fluorescence [8,9], and is 2 times better than previous measurements using higher-order optical processes (two-photon fluorescence [6], Raman scattering [4,5]) despite predictions to the contrary [12,13].To better understand the advantages of this technique and to facilitate ...